Identities vs. Equations in Macroeconomics (Haavelmo)

I have just found a very nice paper by Trygve Haavelmo on identities and equations in macroeconomics. After having received a referee report in which it was written that “identities constrain nothing except our use of language” I searched for some insights that backed up the position that I have in mind. It is always good to be able to write what you think, but standing on the shoulders of others can help a lot. So, I found Haavelmo’s paper:

“Then what interest can it have to study identities in the sense defined above?” […] “The most obvious reason is that we are often unable to see whether what appears to be an equation eventually turns out to be an identity or not.”

This is a point that is raised by Miguel Carrion Alvarez in a recent paper titled The Roads Not Taken: Graph Theory and Macroeconomic Regimes in Stock-Flow Consistent Modelling. In closing a macroeconomic model you have some identities and you have some behavioral equations. So, in reality, what is determined by behavioral relation and what is determined by identity? You might think that these a question that only an academic can find interesting, but there are some real world problems where this is crucial. Think about the macroeconomic regimes in the US and the euro zone. In the US, the government deficit is determined by the behavior of government spending which is based on Keynesian policy-making (more or less). The deficit is whatever it is in order to have the economy run at some socially/politically acceptable level of unemployment. In the Eurozone, the deficits are supposed to be three percent, and since tax rises are ruled out by the political elite government spending is determined by the identity of G = T +3% (all divided by GDP).

Many interesting discussion in macroeconomics revolve around the concept of identities. Savings are equal to investment, spending equal to income, wealth equal to debt. It might be the time for revolutionary change in macroeconomics to make these issues more explicit!

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For instance, S = I. An identity with no behavioral sense. MV = NGDP: false. The original identity is MV = PT, which is true. But there is a lot of transactions T (all without VA) not included in NGDP.